As the RC and DMB say, an enemy behind an obstacle has either partial or superior cover. The example often used is that of a creature fighting behind a portcullis or window (e.g. in DMB page 141). The bit about my ranger having a penalty to attack because the creature has cover or superior cover is clear. What is not clear to me is: does the creature get the same penalty when trying to attack my ranger because now I'm on the other side of the portcullis? Per the rules, I think it should, but it is counterintuitive (at least for ranged attacks). After all, an archer just behind a portcullis is in an ideal position.

Is it just that the borders of the square the creature is standing on aren't considered when determining cover of an enemy? When I thought of that, I wondered about the rules for line of sight, and line of effect for enemies on the other side of a wall, and how the
wall is "between" the squares.

The situation is displayed below: creature o has a penalty to attack rolls against creature x, because creature x is behind a window. Does creature x have a penalty to its attack rolls against o, too?

4 Answers
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Arrow slits: these small openings are designed to provide archers with maximum protection when they fire. An arrow slit grants a ranged attacker superior cover while granting him or her a view of the battlefield. The attacker determines the target's cover as if the attacker were in the square just outside the slit.

@Pat, probably, perhaps there's a concern that accepting your own answer is bad form, especially when posting it a week after accepting a different answer.
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Simon WithersFeb 10 '11 at 3:16

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@simon - Adriano should get the credit for finding his own answer (and a badge I believe). I think its important that we have the correct answer accepted (or at least voted the highest) :) As this is neither, it bugs me.
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Pat LudwigFeb 10 '11 at 3:20

:) Ok, Ok, I'm caving in to the pressure. I thought about accepting my own answer, and it's something I have done -once- on SO, but his answer, while not citing rules, was well constructed.
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Adriano Varoli PiazzaFeb 10 '11 at 12:08

Just to put the focus on determining cover for a ranged attack (from the Dungeon Master Guide):

Attacker’s Burden: For ranged attacks, the attacker has to prove that he has a clear shot. That proof consists of one corner in his space that has clear lines to every corner of the target’s space.

Choose a Corner: The attacker chooses one corner of a square he occupies, and draws imaginary lines from that corner to every corner of any one square the defender occupies. If none of those lines are blocked by a solid object or an enemy creature, the attacker has a clear shot. The defender doesn’t have cover. (A line that runs parallel right along a wall isn’t blocked.)

Cover: If you can’t find a clear shot, the target has cover. No matter which corner in your space you choose, one or two lines from that corner to every corner in the defender’s space are blocked.

Also, from Player's Handbook 1:

Determining Cover: To determine if a target has cover, choose a corner of a square you occupy (or a corner of your attack’s origin square) and trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle or an enemy, the target has cover. (A line isn’t blocked if it runs along the edge of an obstacle’s or an enemy’s square.) If three or four of those lines are blocked but you have line of effect, the target has superior cover.

If a creature is adjacent to a narrow opening on a wall that lays on a square's edge (like the X in your example), I would rule that the creature can choose any corner of its space in order to determine a clear shot (even those that are "in" the wall like the corners 1 and 3). So O have no cover against X's ranged attacks.

Instead, a creature not adjacent to the narrow opening (O) have no clear line to any of X's corners (but has line of effect), so X has superior cover against O's ranged attacks. In this case I don't consider 1 and 3 viable corners for determining a clear line.

This isn't based on the rule book, but on my own logic and how I would treat it if I was a DM.

It really depends on your setting and mode of attack. Some portcullises have slots or openings for ranged are pole-arm attacks so you may want to take that into account. I will divide my answer into both modes of attack.

Ranged Attack:
If you have a window in a wall and creature 0 is standing in the window shooting at creature 1, I see no reason he would have a penalty shooting from it. Creature 1 is standing 30 feet from the window. He now has smaller hit area for hitting creature 0, since he can only hit creature 0's exposed portion through the window. A penalty would be advised.

Melee Attack:
This would vary by weapon. Creature 0 is standing on one side of the window with a sword. Swinging a sword through a window is more challenging. I would advise a penalty for creature 0. Creature 1 is wielding a spear. Spears are long and fit through windows quite easily, but the window is still an obstacle. A lower penalty than creature 0 might be advised.

Who gets cover from whom is, in real world terms, a matter of range, weapon reach, mobility behind the cover, and method of wielding.

In game terms, if you're using a ranged weapon, and they're a ways back, you have cover, they don't. If you're using a melee weapon, both of you have cover. If both of you are back from it, both of you have cover.

Well yes, that's my intuition too. It's just that the rules leave some space for my doubt. Still, I'm just curious. In a game, I don't think I'd penalize an archer behind a window with a -2, it doesn't feel sensible.
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Adriano Varoli PiazzaJan 19 '11 at 10:55

That all depends on how close he is to the window. If he's within the square next to it, no, he's got cover but his target doesn't. (And your cover only matters when you are the target). But if he's 1 square back from it, i'd be looking at angles. At 4, his target has cover, tho less if the target's in the window vs 10' back from it.
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aramisJan 20 '11 at 3:31